TY - JOUR
A1 - Buchin, Kevin
A1 - Buchin, Maike
A1 - Byrka, Jaroslaw
A1 - NĂ¶llenburg, Martin
A1 - Okamoto, Yoshio
A1 - Silveira, Rodrigo I.
A1 - Wolff, Alexander
T1 - Drawing (Complete) Binary Tanglegrams
JF - Algorithmica
N2 - A binary tanglegram is a drawing of a pair of rooted binary trees whose leaf sets are in one-to-one correspondence; matching leaves are connected by inter-tree edges. For applications, for example, in phylogenetics, it is essential that both trees are drawn without edge crossings and that the inter-tree edges have as few crossings as possible. It is known that finding a tanglegram with the minimum number of crossings is NP-hard and that the problem is fixed-parameter tractable with respect to that number.
We prove that under the Unique Games Conjecture there is no constant-factor approximation for binary trees. We show that the problem is NP-hard even if both trees are complete binary trees. For this case we give an O(n 3)-time 2-approximation and a new, simple fixed-parameter algorithm. We show that the maximization version of the dual problem for binary trees can be reduced to a version of MaxCut for which the algorithm of Goemans and Williamson yields a 0.878-approximation.
KW - NP-hardness
KW - crossing minimization
KW - binary tanglegram
KW - approximation algorithm
KW - fixed-parameter tractability
Y1 - 2012
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-124622
VL - 62
ER -